Volume 1, Issue 5
An r-adaptive Finite Element Method for the Solution of the Two-dimensional Phase-field Equations

G. Beckett, J. A. Mackenzie & M. L. Robertson

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Commun. Comput. Phys., 1 (2006), pp. 805-826.

Published online: 2006-01

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  • Abstract

An adaptive moving mesh method is developed for the numerical solution of two-dimensional phase change problems modelled by the phase-field equations. The numerical algorithm is relatively simple and is shown to be more efficient than fixed grid methods. The phase-field equations are discretised by a Galerkin finite element method. An adaptivity criterion is used that ensures that the mesh spacing at the phase front scales with the diffuse interface thickness. 

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@Article{CiCP-1-805, author = {G. Beckett, J. A. Mackenzie and M. L. Robertson}, title = {An r-adaptive Finite Element Method for the Solution of the Two-dimensional Phase-field Equations}, journal = {Communications in Computational Physics}, year = {2006}, volume = {1}, number = {5}, pages = {805--826}, abstract = {

An adaptive moving mesh method is developed for the numerical solution of two-dimensional phase change problems modelled by the phase-field equations. The numerical algorithm is relatively simple and is shown to be more efficient than fixed grid methods. The phase-field equations are discretised by a Galerkin finite element method. An adaptivity criterion is used that ensures that the mesh spacing at the phase front scales with the diffuse interface thickness. 

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7980.html} }
TY - JOUR T1 - An r-adaptive Finite Element Method for the Solution of the Two-dimensional Phase-field Equations AU - G. Beckett, J. A. Mackenzie & M. L. Robertson JO - Communications in Computational Physics VL - 5 SP - 805 EP - 826 PY - 2006 DA - 2006/01 SN - 1 DO - http://dor.org/ UR - https://global-sci.org/intro/cicp/7980.html KW - AB -

An adaptive moving mesh method is developed for the numerical solution of two-dimensional phase change problems modelled by the phase-field equations. The numerical algorithm is relatively simple and is shown to be more efficient than fixed grid methods. The phase-field equations are discretised by a Galerkin finite element method. An adaptivity criterion is used that ensures that the mesh spacing at the phase front scales with the diffuse interface thickness. 

G. Beckett, J. A. Mackenzie & M. L. Robertson. (1970). An r-adaptive Finite Element Method for the Solution of the Two-dimensional Phase-field Equations. Communications in Computational Physics. 1 (5). 805-826. doi:
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